Question: Determine how many solutions exist for the system of equations. ${8x-2y = -16}$ ${4x-y = -8}$
Convert both equations to slope-intercept form: ${8x-2y = -16}$ $8x{-8x} - 2y = -16{-8x}$ $-2y = -16-8x$ $y = 8+4x$ ${y = 4x+8}$ ${4x-y = -8}$ $4x{-4x} - y = -8{-4x}$ $-y = -8-4x$ $y = 8+4x$ ${y = 4x+8}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 4x+8}$ ${y = 4x+8}$ Both equations have the same slope and the same y-intercept, which means the lines would completely overlap. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ Since any solution of ${8x-2y = -16}$ is also a solution of ${4x-y = -8}$, there are infinitely many solutions.